Theoretical Study of Reactivities in Electrophilic Aromatic Substitution

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J. Phys. Chem. A 2003, 107, 2875-2881

2875

Theoretical Study of Reactivities in Electrophilic Aromatic Substitution Reactions: Reactive Hybrid Orbital Analysis Hajime Hirao*,† and Tomohiko Ohwada* Graduate School of Pharmaceutical Sciences, The UniVersity of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan ReceiVed: October 29, 2002; In Final Form: February 4, 2003

Orbital interactions in electrophilic aromatic substitution reactions of anisol, nitrobenzene, and some other analogues were studied. A single frontier orbital (FO), i.e., the HOMO of substituted benzenes, particularly of nitrobenzene, does not account for the regioselectivities of the reaction. We first applied configuration analysis to identify the relative importance of orbital interactions between an electrophile (H+ in this work) and the substituted benzenes. We herein define the reactiVe hybrid orbital (RHO) method for measuring the reactivity of each carbon atom of substituted benzene. An RHO is made by combining all occupied molecular orbitals properly so that the reactivity index for a reaction center, which is similar to superdelocalizability, is maximized. The RHO reactivity indices, λoc, Foc, and F′oc, were shown to predict correctly the experimentally observed regioselectivity and reactivity in the electrophilic aromatic substitution reactions of anisol, nitrobenzene, and other monosubstituted benzenes. Moreover, it was shown that the RHO values for carbon atoms in a polycyclic aromatic hydrocarbon are in good agreement with experimentally determined partial rate factors.

Introduction Electrophilic aromatic substitution is one of the most thoroughly studied reactions in organic chemistry.1-20 It was to this class of reactions that the frontier orbital (FO) theory was applied for the first time by Fukui et al.21,22 Since then, the FO theory has gained general acceptance by the chemical community and has been utilized to interpret reactivities and selectivities of chemical reactions.23 Nevertheless, the FO theory does not predict meta selectivity in the electrophilic substitution of nitrobenzene.1a,11b That is, the highest occupied molecular orbital (HOMO) of nitrobenzene has equivalent amplitudes on the ortho and meta positions as shown below, and thus the FO theory predicts that substitution would occur at both positions.

Therefore, most textbooks of organic chemistry and physical organic chemistry avoid the use of FO theory in this case and attempt to interpret this regioselectivity in terms of stabilization of the intermediate cationic σ-complexes, rather than in terms of orbital interactions.1 The frontier orbitals are canonical MOs, and they are, in general, delocalized over a whole molecule.24 Local characteristics of chemical reactions are not well represented by using such delocalized MOs. This difficulty has been resolved by employing some localized reactive orbitals, such as interaction * E-mail: [email protected], [email protected]. † Present address: Novartis Tsukuba Research Institute, 8 Ohkubo, Tsukuba, Ibaraki 300-2611, Japan.

frontier orbitals (IFOs)25 and projected reactive orbitals (PROs),26 which have been developed by Fujimoto et al. These orbitals include all the MOs relevant to the interaction of a reactant with a putative reagent, making it possible to see what part of the reactant participates actively in electron delocalization and what changes in bonds will be brought about in the reaction.25,26 Accordingly, it is inappropriate to analyze molecular reactivities in terms of a single FO and it is therefore not surprising that the FO theory fails to predict selectivity of some chemical reactions. Although the IFO method can afford a means of extracting orbital interactions compactly in terms of paired orbitals of the reagent and reactant moieties by analyzing the wave function of an interacting system,25 the PRO method 26 developed for a reactant molecule in an isolated state is more suitable for practical purposes, e.g., prediction of reactivities and selectivities of chemical reactions. In the PRO method, the reference function is defined as the AO contributions of the reaction center out of the HOMO or IFO of a minimum molecule of the relevant functional groups, and the function has been commonly applied to molecules bearing substituents for obtaining reactive orbitals.26 Unfortunately, this scheme limited the objects of analysis by means of the PRO method to molecules having very similar structures.26 Therefore, in this paper, we propose a novel method to obtain a reactive orbital without use of a reference function. The present method provides a reactive IFO-like orbital that is well localized around a reaction center and its energy level is high; therefore electron delocalization toward a reagent can most efficiently take place through the orbital, which we will call the reactive hybrid orbital (RHO). The purpose of this paper is therefore 2-fold: (1) to clarify the fundamental orbital interactions in electronic aromatic substitution reactions and (2) to introduce a practical method for obtaining a reactive orbital to estimate local reactivity of molecules. The reactivity indices obtained here measure the

10.1021/jp027330l CCC: $25.00 © 2003 American Chemical Society Published on Web 04/02/2003

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power of a reaction center to donate electrons toward an unoccupied reactive orbital of a reagent. It should also be noted that construction of reliable reactivity indices is, in a practical sense, an important task in basic organic chemistry, as well as in applied chemistry such as medicinal chemistry, where trustworthy quantitative structure-activity relationships (QSAR) are essential to the success of computerassisted drug designs.27 In particular, the electronic factor discussed in this paper is considered to be one of the most fundamental and significant components determining SAR.27 Calculations Energetically stable geometries of anisol and nitrobenzene were located on potential energy surfaces at the RHF/6-31G* level using the Gaussian 98 program.28 Vibrational frequency analyses were also performed to confirm that obtained structures correspond to energy minima. The wave functions and MOs calculated at the RHF/6-31G*//RHF/6-31G* or RHF/3-21G// RHF/6-31G* level were then analyzed to get a deeper understanding of interactions between reagent and reactant, as explained in detail in the next section. Orbital representations were created with MOLEKEL 4.2, using a contour value of 0.055.29 Results and Discussion Configuration Analysis of the Interaction between Electrophile and Benzenes. In textbooks, orbital interactions are usually described in terms of canonical molecular orbitals.1 Thus, we utilized those orbitals initially to analyze the orbital interactions in electrophilic aromatic substitution. To identify how importantly each MO participates in the orbital interaction with an electrophile (H+ in this analysis), configuration analysis30 has been performed. The analysis expands the wave function of the combined system of a reagent and a reactant in terms of possible electronic configurations of two fragments denoted here by q,

Ψ ) C0Ψ0 +

∑q CqΨq

(1)

where Ψ0 indicates the electron configuration in which the two fragments retain their original electron configurations in an isolated state, and Ψq represents an electron-transferred configuration between the two fragments or an electron-excited configuration within the same fragment. To show that not only the HOMO, but also other π-type occupied MOs participate significantly in electron delocalization in aromatic substitutions, we take a simple model system, wherein a proton as an electrophile is located 1.5 Å above the carbon atoms of the ortho, meta, or para positions of the geometry-optimized benzenes.31 In Figure 1, the π-type canonical MOs of anisol and nitrobenzene are shown. Basically, coefficients Cq for the electrontransferred configurations in which a single electron is shifted from occupied π MOs of the benzenes to unoccupied MOs of an electrophile (H+) have nonzero values, whereas the contributions from other configurations are negligible.30 Table 1 shows the coefficients for one-electron-transferred configurations, in which an electron is shifted from an occupied π-type MO of the anisol or nitrobenzene fragment to the LUMO of the H+ fragment. Upon perturbation of the π MOs of benzene, illustrated in Chart 1, by a substituent, the degeneracy of π2 and π3 is removed. As a consequence, π2 becomes the HOMO in the case

Figure 1. π-type canonical MOs (RHF/6-31G*//RHF/6-31G*) and their energy levels (in hartrees) calculated at the RHF/6-31G*//RHF/ 6-31G* and RHF/3-21G//RHF/6-31G* (in parentheses) levels for anisol and nitrobenzene.

TABLE 1: Absolute Values of Coefficients of the One-Electron-Transferred Electron Configurations from the MOs in Anisol, Nitrobenzene, or Benzene to the LUMO of H+ Calculated at the RHF/6-31G*//RHF/6-31G* and RHF/3-21G//RHF/6-31G* (in Parentheses) Levels |Cifl| i (π MO)

ortho

l (LUMO of H+) meta

para

ψ29 (π2-type)b ψ28 (π3-type) ψ27 ψ23

Anisola 0.231 (0.236) 0.234 (0.233) 0.342 (0.345) 0.313 (0.314) 0.100 (0.093) 0.158 (0.161) 0.090 (0.101) 0.081 (0.095)

0.413 (0.412) 0.036 (0.038) 0.157 (0.163) 0.067 (0.080)

ψ32 (π3-type)b ψ31 (π2-type) ψ26

Nitrobenzene 0.370 (0.373) 0.349 (0.351) 0.152 (0.154) 0.203 (0.205) 0.153 (0.158) 0.144 (0.150)

0.000 (0.000) 0.415 (0.419) 0.146 (0.151)

ψ21 (π2)b ψ20 (π3)b ψ17

Benzenec 0.196 (0.197) 0.196 (0.197) 0.356 (0.359) 0.356 (0.359) 0.155 (0.160) 0.155 (0.160)

0.421 (0.424) 0.000 (0.000) 0.155 (0.160)

a The values for the ortho and meta positions on the same side as the methoxy group. b The HOMO. c For benzene, the position over which the amplitude of the π2 MO was the largest was considered to be the para position.

CHART 1: Degenerate HOMOs and LUMOs of Benzene

of anisol and π3 becomes the HOMO in the case of nitrobenzene (Figure 1). As can be seen in Table 1, not only the HOMO but also the other π-type orbitals participate in the orbital interactions. In particular, in the cases of ortho and meta substitutions of anisol and para substitution of nitrobenzene, the contribution of the HOMO-1 to the interaction is larger than that of the HOMO. In Table 2, the most important occupied MOs in

Reactivity in Electrophilic Aromatic Substitutions TABLE 2: Summary of Orbital Interactions in Anisol and Nitrobenzene the most important MO in orbital interactionsa

J. Phys. Chem. A, Vol. 107, No. 16, 2003 2877 SCHEME 1: Orbital-Mixing Patterns in Anisol and Nitrobenzenea

the MO determining regioselectivityb

ortho meta para

Anisol HOMO-1 HOMO-1 HOMO

HOMO HOMO HOMO

ortho meta para

Nitrobenzene HOMO HOMO HOMO-1

HOMO-1 HOMO-1 HOMO-1

a Identified by configuration analysis. See Table 1 and the text for detail. b Interpreted by the orbital mixing rule. See ref 32.

interactions with an electrophile, as identified by analysis of the wave function, are summarized. It has been found that both in anisol and in nitrobenzene, the π3-type MO plays the most significant role in the orbital interactions for ortho and meta substitutions, irrespective of the height of the energy level relative to the π2-type MO. In para attack, however, the π2type MO takes part most significantly in the orbital interaction with an electrophile. For reference, we also tabulated the Cq values for benzene (Table 1). In benzene, all the positions are equivalent and it is meaningless to assign any position as ortho, meta, or para; however, because our main purpose here is to understand orbital interactions in benzenes, we defined these positions in benzene on the basis of MO amplitudes (see Table 1). In the case of benzene, we see that the π3 MO interacts more strongly with an electrophile than the π2 does in ortho and para attacks. The results suggest that, in general, the π3type MO plays the most important role in the orbital interaction in ortho and meta substitutions, whereas in para substitution, the π2-type MO plays the most significant role. Furthermore, the origin of the regioselectivity might be ascribed to orbital mixing between the π2 and π4 MOs of benzenes (see Chart 1) through intervention of the orbital of the substituent.32 The mixing relation among the coefficients of π2, π4, and the fragment orbital of a substituent is determined by the relative heights of the energy levels of these orbitals. In Scheme 1, orbital mixing of the fragment orbitals in anisol and nitrobenzene is summarized. In the case of anisol, the energy level of the occupied orbital of the substituent fragment (-OH) is lower than that of π2 of benzene, whereas in the case of nitrobenzene, the energy level of the unoccupied orbital of the substituent fragment (-NO2) is between those of π2 and π4. As a result, the amplitude of the HOMO (π2-type) increases around the ortho and para positions in anisol, whereas that around the meta position is reduced, compared with π2 of benzene. The HOMO-1 (π3-type) remains almost unaffected in anisol. In contrast, although the HOMO (π3-type) is unaffected by -NO2 in nitrobenzene, the amplitude of HOMO-1 (π2-type) is reduced around the ortho and para positions and is enhanced around the meta position. The change in amplitude of π2 MOs by the perturbation can be detected in the orbital amplitudes shown in Figure 1. Therefore, the MOs giving rise to the difference in relative reactivity between the ortho and meta positions of anisol and nitrobenzene are different from those that participate most strongly in orbital interactions, as summarized in Table 2. On the other hand, the absolute reactivity of each position is determined by the electron-donating ability from several π-type orbitals. Hence, it is unreasonable and impossible to attempt to explain the reactivity of aromatic substitution solely in terms of the FO; rather, the multiple π orbitals of benzenes are apparently relevant to the reactivities.

a As a result of orbital mixing, the amplitude of the π -type MO in 2 the + region is increased, whereas that in the - region is reduced.

Orbital mixing would modify the components of a reactive orbital that is built from π-type canonical MOs, thereby leading to a difference in reactivity depending on the reaction site. Definition of Reactive Hybrid Orbital and Interpretation of Regioselectivities of Electrophilic Aromatic Substitution. Our next step was to develop a method for obtaining a reactive orbital for practical use. Like a situation where a hybrid atomic orbital is used, it is clearer to see orbital interactions in terms of a single hybrid MO rather than in terms of all of the relevant canonical MOs, under the conditions that the original forms of the canonical MOs are unchanged. Furthermore, the composition of the hybrid MO should be informative as the configuration analysis, i.e., relative importance of the contribution of canonical MOs being well-characterized. In addition, the hybrid MO should be consistent with local characteristics of chemical interactions. It was shown that the IFO method gives a practical way of deriving those hybrid MOs fulfilling these requirements, starting from the canonical MOs of the reactant and reagent fragment molecules.25 However, a method that gives hybrid MOs without using the reagent MOs seems more useful in a practical sense for comparing reactivities of the reactant molecules. Thus, we develop such a method for obtaining a well-behaved reactive orbital called the reactive hybrid orbital (RHO). When an electron-donating orbital φoc is represented by a linear combination of canonical occupied MOs as oc

φoc ) (

∑i

oc

diψi)/(

∑i di2)1/2

(2)

the energy level of the orbital can be evaluated by oc

oc

∑i di2i)/(∑i di2)

λoc ) (

(3)

where i is the energy level of the canonical MO ψi obtained by solving a Hartree-Fock-Roothaan equation. The orbital φoc is then represented by a linear combination of atomic orbitals

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(LCAO) as

φoc )

∑µ Cµχµ

(4)

If we extract only the terms containing the AOs on the atom of the reaction center (denoted here by A) from eq 4:

φ′oc )

∑Cµχµ

(5)

µ∈A

then we can define a site electron density foc and an index Foc, respectively, as

foc ) 〈φoc|φ′oc〉

(6)

Foc ) - foc/λoc

(7)

and

The value 2foc corresponds to the electrons in φoc belonging to atom A, and the formula of Foc is similar to that of superdelocalizability based on the Hu¨ckel approximation.33 We obtained a set of di values in eq 2, which gives the maximum value of Foc, by minimizing 1/Foc numerically with the DavidonFletcher-Powell method.34 The orbital φoc represented by eq 2 with the optimized di values is specifically called an occupied RHO. The reactivity of the electron-donating center can also be evaluated on the basis of the RHO obtained above by

F′oc ) - f ′oc/λoc

(8)

f ′oc ) 〈φ′oc|φ′oc〉

(9)

where f oc ′ is defined as

Note that 2f oc ′ , unlike 2 foc, does not count electrons in the internuclear region which are used for bonding with the adjacent atoms, e.g., the π-bonding region in the case of the aromatic π orbitals. Thus F′oc is more similar to superdelocalizability than Foc is.35 The occupied RHO is a high-lying orbital (i.e., a negatively small λoc value), but it is localized on the reaction center (i.e., a large foc value). Although the RHO method owes some of the fundamental ideas to the projected reactive orbital (PRO) method,26 they are essentially different from each other. For clarity, it seems worth explaining the difference between the two methods. In the PRO method, a reference function δr of a reactant, which is assumed to represent most approximately a transient bond with a reagent, is defined prior to calculations. However, determination of the reference function needs a somewhat arbitrary selection of AOs. Furthermore, projection of a reference function represented by a few AOs only on a reaction center extracted from the HOMO or IFO of a molecule results in a low-energy PRO as compared with an interaction frontier orbital.26 Though the set {di} of eq 2 was determined by projection of a reference function δr in the PRO method, we directly optimize {di} in the RHO method; therefore an RHO can be calculated without the concept of a reference function. By using the present method, a reactive orbital can be uniquely obtained even in complicated cases where a split valence basis set such as 6-31G* or 3-21G(*) is used. It should also be noted that a related method, which determines δr that gives the maximum value of λoc, was proposed by Kurita and Takayama.36 Their method localizes a reactive orbital by imposing a limitation on δr within an AO space of a molecule. The reference function δr cannot contain

Figure 2. Contour plot of the RHO at each point calculated at the RHF/6-31G*//RHF/6-31G* level. RHO values, λoc, foc, Foc, f ′oc and F′oc calculated at the RHF/6-31G*//RHF/6-31G* and RHF/3-21G//RHF/631G* (in parentheses) levels are also shown.

d-type AOs in generating a reactive orbital for the formation of new chemical bonds with electrophiles.36 Also, localization of a reactive orbital calculated by their method, particularly for a conjugated or aromatic system is insufficient, despite the limitation mentioned above. This is because their method focuses on the energy level of a reactive orbital and pays less attention to the localizability of the orbital. Although their method made some improvement over the original PRO method in that it offered a procedure for determining a reference function in a unique, analytical manner, the meaning of a reference function became less clear. These seem to indicate inadequacy of the concept of a reference function; hence development of a method for deriving a reactive orbital without the concept is important. In Figure 2, the RHOs for ortho, meta, and para attacks in anisol and nitrobenzene are depicted. In all cases, the RHOs have the largest amplitude around the reaction center, but they are not localized completely on the reaction center. They also have amplitudes around the adjacent two carbons and have an out-of-phase amplitude around the carbon at the 4-position with respect to the reaction center. This suggests that the AOs on multiple carbon atoms of the benzene system, in addition to the reaction center, participate in the aromatic reaction.

Reactivity in Electrophilic Aromatic Substitutions

J. Phys. Chem. A, Vol. 107, No. 16, 2003 2879

TABLE 3: Absolute Values of LCMO Coefficients of the RHOs in the Ortho, Meta, and Para Positions in Anisol, Nitrobenzene, and Benzene Calculated at the RHF/6-31G*// RHF/6-31G* and RHF/3-21G//RHF/6-31G* (in Parentheses) Levels ortho

meta

log(PRF) substituent

LCMO coefficient of RHO π MOa

TABLE 4: Comparison of the RHO Values (RHF/6-31G*) and Partial Rate Factors (PRFs) for Aromatic Substitution Reactionsa

para

ψ29 (π2-type)c ψ28 (π3-type) ψ27 ψ23

Anisolb 0.495 (0.500) 0.508 (0.504) 0.771 (0.769) 0.700 (0.698) 0.275 (0.246) 0.435 (0.425) 0.279 (0.298) 0.246 (0.277)

0.871 (0.862) 0.082 (0.089) 0.436 (0.439) 0.211 (0.237)

ψ32 (π3-type)c ψ31 (π2-type) ψ26

Nitrobenzene 0.811 (0.811) 0.771 (0.771) 0.361 (0.361) 0.475 (0.475) 0.450 (0.448) 0.422 (0.423)

0.000 (0.000) 0.901 (0.902) 0.434 (0.431)

ψ21 (π2)c ψ20 (π3)c ψ17

Benzened 0.451 (0.451) 0.451 (0.451) 0.781 (0.782) 0.781 (0.782) 0.432 (0.431) 0.432 (0.431)

0.902 (0.902) 0.000 (0.000) 0.432 (0.431)

H p-OCH3 p-Me p-tBu p-Ph m-tBu m-Me p-F p-Cl m-F m-Cl m-NO2 p-NO2 a

λoc

Foc

F′oc

-0.362 -0.345 -0.354 -0.354 -0.357 -0.358 -0.360 -0.367 -0.374 -0.378 -0.381 -0.398 -0.404

1.346 1.474 1.392 1.385 1.361 1.351 1.339 1.368 1.301 1.254 1.266 1.243 1.142

0.704 0.824 0.743 0.736 0.719 0.705 0.694 0.741 0.682 0.636 0.652 0.653 0.558

mercuration nitration chlorination 0.0 3.36 1.37 1.24 0.81 0.53 0.35 0.47 -0.44 -1.41 -1.22 -

0.0 1.69 1.76 1.27 0.58 0.32 -0.11 -0.89 -3.08 -6.79 -8.14

0.0 7.67 2.91 2.60 2.78 0.73 0.69 0.64 -0.42 -2.44 -2.85 -

Experimental values taken from refs 3c and 4. See also refs 3d-f.

a See Figure 1. b The values for the ortho and meta positions on the same side as the methoxy group. c The HOMO. d For benzene, the position over which the amplitude of the π2 MO was the largest was considered to be the para position.

Table 3 summarizes the LCMO coefficients of the RHOs in the ortho, meta, and para positions. In anisol, the HOMO (π2type) is the major component of the RHO only in the case of para attack. On the other hand, in nitrobenzene, the HOMO (π3-type) is the most important in the cases of ortho and meta attacks. In both compounds, ortho and meta attacks of an electrophile are facilitated mainly by electron delocalization from the π3-type MOs, whereas para attacks are facilitated by that from the π2-type MOs. In addition, the LCMO coefficient of π3 of benzene is the largest in ortho and meta substitutions and that of π2 is largest in para substitution. From these results, it can be understood that the RHOs showed trends in the relative importance of canonical MOs similar to the results of configuration analysis. Therefore, it appears that the complicated orbital interactions shown in Table 1 are condensed compactly and appropriately to a single hybrid MO, i.e., the RHO, which takes part in electron delocalization toward an electrophile. Calculated RHO parameters, i.e., λoc, foc, Foc, f′oc, and F′oc defined above for these compounds, are also presented in Figure 2. In anisol, the RHO energy level λoc is lower and Foc is larger in the ortho and para positions than those in the meta position, predicting that electrophilic substitution will occur in the ortho and para positions. On the other hand, in nitrobenzene, the values predict meta regioselectivity. These predictions are consistent with experimental results.1 In the case of benzene, the values are identical in all positions. Interestingly, it was also predicted that anisol is more reactive in the para position than benzene but less reactive in the meta position, which is consistent with the signs of the σp+ and σm constants for anisol.27 Reactivities of Monosubstituted Benzenes and Policyclic Aromatic Hydrocarbons. Now let us apply the RHO method to monosubstituted benzenes (Table 4), experimentally examined. In Table 4, we summarize the results of RHO calculations (RHF/6-31G*) and logarithms of the partial rate factors (log(PRF)) for mercuration,3d nitration,3c,e,4,37 and chlorination3f of some monosubstituted benzenes. One sees that the RHO indices are on the whole in good agreement with the reaction rates. In Figure 3, λoc values are plotted against log(PRF) values, demonstrating that λoc is closely correlated with log(PRF).

Figure 3. Relationship between the RHO energy level λoc and logarithms of the partial rate factors (log(PRF)) for mercuration, nitration, and chrorination of monosubstituted benzenes.

We next apply the RHO method to larger systems. It was pointed out that the FO theory often fails for large systems such as polycyclic aromatic ones.24 The RHO values (RHF/6-31G*) for carbon atoms for benzene, naphthalene, and anthracene were calculated and compared with the magnitude of the experimentally determined partial rate factors for protiodetritiation (Table 5).5b The RHO indices are consistent with not only regioselectivity but also the difference in reactivity among molecules of different sizes. The number of occupied π orbitals increases with the increase in the size of a molecule. Additionally, the energy gap between these π orbitals are reduced as compared with those in benzene. These lead to the increase in the relative importance of MOs other than the FO (HOMO), which is taken into consideration in the present method. Table 6 presents the LCMO coefficients of RHOs. The R regioselectivity in electrophilic aromatic substitution in naphthalene was successfully predicted by FO theory.21 In fact, the present analysis showed that the HOMO plays the most important role in the R attack (Table 5). Furthermore, it is interesting to note that other lowlying MOs also play active roles in R attack, and in β attack, the HOMO-1 plays a more important role than the HOMO does. Before concluding, we discuss the relevance of our new approach to the critiques of FO theory.11b,24 The FO theory accounted for the orientation of substitution rather than relative rates of substitution in different alternant hydrocarbons. As

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TABLE 5: Comparison of the RHO Values Calculated at the RHF/6-31G*//RHF/6-31G* Level and Partial Rate Factors (PRFs) of Protiodetritiation of Benzene, Naphthalene, and Anthracene in CF3CO2H at 70 °Ca hydrocarbon

position

λoc

Foc

F′oc

log (PRF)b

benzene naphthalene

1 1 2 1 2 9

-0.362 -0.351 -0.355 -0.348 -0.351 -0.327

1.346 1.379 1.363 1.378 1.372 1.464

0.704 0.738 0.723 0.740 0.734 0.814

0.00 3.07 2.18 3.90 3.05 7.10

anthracene

a

b

Data taken from ref 5b. See also refs 9a and 9b.

TABLE 6: Absolute Values of LCMO Coefficients of the RHOs on Carbon Atoms in Policyclic Aromatic Hydrocarbons Calculated at the RHF/6-31G*//RHF/6-31G* Level naphthalene

anthracene

MO

C1

C2

C1

C2

C9

HOMO HOMO-1 HOMO-2 HOMO-3 HOMO-4 HOMO-5 HOMO-6 HOMO-7 HOMO-8 HOMO-9 HOMO-10

0.725 0.009 0.533 0.320 0.297 -

0.505 0.619 0.268 0.475 0.251 -

0.578 0.015 0.586 0.353 0.240 0.311 0.206

0.486 0.504 0.358 0.174 0.464 0.330 0.164

0.775 0.475 0.308 0.282

shown above, we found a good correlation of the calculated RHO indices to the magnitude of the experimental partial rate factors for polyaromatic molecules. This suggests that our approach could be extended to comparison with divergent molecules. The FO theory does not always predict regioselectivies; nitrobenzene is a representative example, as discussed in this paper. Our approach has also been shown to overcome this problem by taking into account all relevant MOs properly. Finally, we analyze reactivities in terms of a single hybrid MO, rather than in terms of the relevant MOs separately. Thus, we can obtain outcomes of calculation in the simplest format, which has been the major reason for the success of the FO theory.24 Conclusion It has been shown that in many cases of electrophilic aromatic substitution, the FO does not always play the most important role, indicating that the importance of the HOMO should not be exaggerated, and other MOs should also be taken into consideration. In anisol, ortho, meta, and para substitutions are facilitated mainly by electron delocalization from the HOMO1, HOMO-1, and HOMO, respectively, whereas in nitrobenzene, they are facilitated by the HOMO, HOMO, and HOMO1, respectively. As a result of orbital mixing, the amplitude of the HOMO of anisol and that of the HOMO-1 of nitrobenzene are changed, as compared with π2 of benzene, leading to regioselectivity. Thus, the reactivity of the ortho, meta, and para positions of substituted benzenes can be evaluated only by taking into account all the relevant MOs that should participate in interactions with an attacking electrophile. It has also been demonstrated that the orbital interactions can be reasonably described not by a single FO but by a single reactive orbital

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J. Phys. Chem. A, Vol. 107, No. 16, 2003 2881 to clarify the origin of the latter that is also an important driving force of a reaction between reactant and reagent. We believe that the conclusion drawn by taking the simple model reflects the fundamental aspect of orbital interactions in aromatic systems, to which many kinds of reagents have been shown to attack. For study of substituent effects of aromatic compounds in terms of molecular electrostatic potentials, see for example ref 14 and: Gadre, S. R.; Suresh, C. H. J. Org. Chem. 1997, 62, 2625. For discussions from the HSAB viewpoint, see, for example, refs 12 and 17. (32) (a) Inagaki, S.; Fukui, K. Chem. Lett. 1974, 509. (b) Inagaki, S.; Fujimoto, H.; Fukui, K. J. Am. Chem. Soc. 1976, 98, 4054. (33) Fukui, K.; Yonezawa, T.; Nagata, C. Bull. Chem. Soc. Jpn. 1954, 27, 423. (34) (a) Fletcher, R.; Powell, M. J. D. Comput. J. 1963, 6, 163. (b) Reddy, P. J.; Zimmermann, H. J.; Hussain, A. J. Comput. Appl. Math. 1975, 1, 255. (35) The orbital φoc obtained by maximizing F′oc resulted in a similar orbital to φoc gained by maximizing Foc. However, if this procedure (maximization of F′unoc) was followed in the unoccupied MO space to obtain an unoccupied RHO φunoc, imbalance in amplitude of φunoc occurred in many cases. Therefore, we decided to adopt the procedure that maximizes Foc or Funoc for calculating an RHO. (36) Kurita, Y.; Takayama, C. J. Phys. Chem. A 1997, 101, 5593. (37) HNO3-CH3NO2 or HNO3-Ac2O and at 0 °C or 25 °C (substituents except -NO2, see ref 3e) and HNO3-H2SO4, 25 °C (in the case of NO2, see ref 4). (38) Karelson, M.; Lobanov, V. S.; Katritzky, A. R. Chem. ReV. 1996, 96, 1042.